Preheat oven to 350 degrees and spray six 8" cake pans with non-stick cooking spray. Set aside.
Using a standing mixer, blend the butter, eggs, milk and yogurt together until incorporated. Add the dry cake mix and blend with the mixer speed on low. Scrape the sides of the bowl and mix again on medium speed until smooth.
Divide batter evenly into six large bowls and add one color of dye to each bowl. Mix thoroughly, until colors are evenly distributed. Divide batter evenly between the cake pans and evenly spread each pan of batter using a spatula. Bake 40-45 minutes, until a toothpick inserted in the center of each cake comes out clean. Cool cakes completely on a wire rack.
To make the frosting, combine the butter and yogurt together in the bowl of a standing mixer. Blend until smooth, then slowly add each frosting mix and blend together until creamy.
Cut a 4-inch circle out of the center of 2 cake layers using a round cookie cutter.
To assemble the cake, place the pink intact cake on a large cake stand, then spread the top with frosting. Frost the top using an offset spatula or butter knife. Position one of the cake rings on top. Spread frosting over the top and inside the circle. Repeat with second cake ring. Fill the hole with sprinkles (can include candies if desired). Place remaining cake layer on top. Frost the top and sides of the entire cake.
Use a butter knife or spatula to frost cake completely, then garnish with rainbow sprinkles.